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Simplifying 2.5x2 + 0.6x = 3480 Reorder the terms: 0.6x + 2.5x2 = 3480 Solving 0.6x + 2.5x2 = 3480 Solving for variable 'x'. Reorder the terms: -3480 + 0.6x + 2.5x2 = 3480 + -3480 Combine like terms: 3480 + -3480 = 0 -3480 + 0.6x + 2.5x2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -1392 + 0.24x + x2 = 0 Move the constant term to the right: Add '1392' to each side of the equation. -1392 + 0.24x + 1392 + x2 = 0 + 1392 Reorder the terms: -1392 + 1392 + 0.24x + x2 = 0 + 1392 Combine like terms: -1392 + 1392 = 0 0 + 0.24x + x2 = 0 + 1392 0.24x + x2 = 0 + 1392 Combine like terms: 0 + 1392 = 1392 0.24x + x2 = 1392 The x term is 0.24x. Take half its coefficient (0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. 0.24x + 0.0144 + x2 = 1392 + 0.0144 Reorder the terms: 0.0144 + 0.24x + x2 = 1392 + 0.0144 Combine like terms: 1392 + 0.0144 = 1392.0144 0.0144 + 0.24x + x2 = 1392.0144 Factor a perfect square on the left side: (x + 0.12)(x + 0.12) = 1392.0144 Calculate the square root of the right side: 37.309709192 Break this problem into two subproblems by setting (x + 0.12) equal to 37.309709192 and -37.309709192.Subproblem 1
x + 0.12 = 37.309709192 Simplifying x + 0.12 = 37.309709192 Reorder the terms: 0.12 + x = 37.309709192 Solving 0.12 + x = 37.309709192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = 37.309709192 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = 37.309709192 + -0.12 x = 37.309709192 + -0.12 Combine like terms: 37.309709192 + -0.12 = 37.189709192 x = 37.189709192 Simplifying x = 37.189709192Subproblem 2
x + 0.12 = -37.309709192 Simplifying x + 0.12 = -37.309709192 Reorder the terms: 0.12 + x = -37.309709192 Solving 0.12 + x = -37.309709192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = -37.309709192 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = -37.309709192 + -0.12 x = -37.309709192 + -0.12 Combine like terms: -37.309709192 + -0.12 = -37.429709192 x = -37.429709192 Simplifying x = -37.429709192Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.189709192, -37.429709192}
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